I'm not sure that this page should exist. The "Multivariate gamma distribution" is not a generalization of the Wishart in the sense that it contains a larger family of distributions. Instead, for any parameterization of the multivariate gamma we can obtain an equivalent Wishart distribution by absorbing beta into the scale matrix, pulling out 1/2, and adjusting the degrees of freedom. At best, it is an alternate parameterization of the Wishart and should be described as such. It certainly doesn't match the situations similar to how the t generalizes the Cauchy, how the Pitman–Yor generalizes the Dirichlet process, or how the Gamma generalizes the exponential.
An entire chapter of the reference "Continuous Multivariate Distributions" by Kotz, Balakrishnan, and Johnson is devoted to the Multivariate gamma distribution so the page can and should exist. The distribution generalizes the univariate gamma distributions. However, the authors state "it is a rather daunting task to attempt to present a coherent, properly classified and an organized description of multivariate gamma distributions, due to an abundance of isolated and disconnected results and substantial time stretches during which little research was carried out in this area followed by booming research activity." Whether or not the current Wikipedia article on this distribution is a reasonable summary is a different question. Mathstat (talk) 16:08, 16 April 2012 (UTC)
Strange that the article doesn't cite "Continuous Multivariate Distributions" by Kotz, Balakrishnan, and Johnson. After all Wikipedia convention is to state more than one citation where possible. But note that the title of the chapter is "Multivariate Gamma Distributions", and the book has sections for 21 named varieties (13 of which are (only?) bivariate). Is this form stated one of them? Melcombe (talk) 21:01, 16 April 2012 (UTC)
Also strange that the only reference cited: Iranmanesha, Anis, M. Arashib and S. M. M. Tabatabaeya (2010). "On Conditional Applications of Matrix Variate Normal Distribution". Iranian Journal of Mathematical Sciences and Informatics, 5:2, pp. 33–43. happens to be the only reference cited in another new article Inverse multivariate gamma distribution and one of only two cited in another new article Matrix t-distribution (and who knows how many others). (Will check later if this variant of MV Gamma is mentioned in the Kotz et al. volume or cited by any other authors.) Mathstat (talk) 22:52, 16 April 2012 (UTC)
Multivariate gamma distribution should be an article but not this article. This article is about one particular definition of a matrix-variate gamma distribution, not a multivariate gamma distribution. Look at the support set and density. Multivariate gamma should have support on . "Continuous Multivariate Distributions" (2e) mentions no matrix variate gamma distribution called multivariate gamma. The article is not correctly named and should be moved to a page with a different title (without a redirect), or removed. Mathstat (talk) 19:04, 17 April 2012 (UTC)
I have now renamed the two articles to have matrix instead of multivariate (but leaving redirects for now). However, it seems from this_paper, at least, that "multivariate gamma" has been used for matrix-valued rvs as in this artice. But, it seems good to make the distinction and to follow the naming for the matrix-t. Melcombe (talk) 23:37, 22 May 2012 (UTC)